On January 1, Welling Company purchased 100 of the $1,000 face value, 8%, 10-year bonds of Mann, Inc. The bonds mature on January 1 in 10 years, and pay interest annually on January 1. Welling purchased the bonds to yield 10% interest. Information on present value factors is as follows:

Present value of $1 at 8% for 10 periods

0.4632

Present value of $1 at 10% for 10 periods

0.3855

Present value of an annuity of $1 at 8% for 10 periods

6.7101

Present value of an annuity of $1 at 10% for 10 periods

6.1446
How much did Welling pay for the bonds?

A. $95,477
B. $100,000
C. $92,230
D. $87,707

D. $87,707

Explanation:

The present value of the investment is the sum of the value of the periodic cash interest payments and the value of the bond proceeds at maturity.

The interest payment at 8% on each bond = $1000 × 8% = 1000 × 0.08 = $80 per year for 10 years.

Applying a present value factor of 6.1446 (Present value of an annuity of $1 at 10% for 10 periods) gives a present value of the periodic interest payments of (6.1446 × $80) = $491.57.

The proceeds of each bond at maturity = face value × present value factor of 0.3855 (Present value of an annuity of $1 at 10% for 10 periods) = $1000 × 0.3855 = $385.5.

The total price for the bond =  (The proceeds of each bond at maturity + the periodic interest payments) × 100 bonds

= ($491.57 + $385.50) × 100 bonds = $87,707.

Therefore welling would pay $87,707 for the bonds.